Finite Group Reduction of the DR/DZ Hierarchies

2026/07/18 by Si-Qi Liu, Youjin Zhang, Tianwen Zhong · 1 citation
#math.AG #math-ph #math.MP

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Abstract

We show that the finite group reduction of the Dubrovin-Zhang/Double Ramification hierarchy associated to a semisimple CohFT preserves its bihamiltonian structure and its tau structure. By applying this result to the orbifold Gromov-Witten theory with the target ℙ¹_2,2,2,2, we see that there are two different and interesting integrable hierarchies that can be associated to the Frobenius manifold structure on the Hurwitz space M_1;1. One of them is equivalent to the genus 1 topological recursion.

Cited by

• Lifts of partial cohomological field theories and examples of bi-Hamiltonian structures in the non-semisimple case

Related

• The bihamiltonian structures of the DR/DZ hierarchies at the approximation up to genus one
• Bihamiltonian structure of the DR hierarchy in the semisimple case
• Frobenius structures on double Hurwitz spaces
• On the strong DR/DZ equivalence conjecture
• Genus zero Whitham hierarchy via Hurwitz--Frobenius manifolds